In recent years, active flow control has been used to increase the aerodynamic efficiency of machines having air flow over a surface, in particular vehicles such as airplanes. Adverse fluid flows generated over aerodynamic surfaces can buffet and fatigue downstream structures exposed to the flows, and the flows can affect efficiency by increasing drag or resistance over the surface. In one version of active flow control, jets of air are blown into the path of the adverse fluid flows to mix with the flows and cause the air to flow more smoothly over the aerodynamic surfaces and reduce the drag and resistance over the surfaces or increase the lift force generated by the surfaces. In many cases, such active flow control can be implemented in existing vehicle designs without needing significant changes thereby directly reducing the operating cost of the vehicle or other machine.
One device for creating jets of air in active flow control is a synthetic jet actuator that forms a so called synthetic jet flow by moving air back and forth through a small opening of the device. Synthetic jet actuators typically have a housing in the shape of a hollow box or cylinder with a resonant chamber therein and an orifice or nozzle opening through one of the side or end walls. At least one wall of the synthetic jet is formed from a flexible membrane that can deflect inwardly and outwardly to alternately decrease and increase the volume in the resonant chamber and expel and draw in air through the opening. Deflection of the membrane may be caused by a piezoelectric actuator that responds to an applied electric field.
The piezoelectric actuator may include a piezoceramic plate or disk having a surface facing and rigidly attached to a corresponding surface of the membrane. The actuator may have a single piezoceramic disk attached to a surface of the membrane, or two piezoceramic disks with each disk being attached in a similar manner to one of the opposing surfaces of the membrane. In alternative arrangements, a piezoelectric strain amplification structure, such as that shown in U.S. Pat. No. 8,937,424, issued to Griffin et al. on Jan. 20, 2015, and entitled, “Strain Amplification Structure and Synthetic Jet Actuator,” may be implemented to cause the membrane to deflect inwardly and outwardly.
A synthetic jet actuator works most efficiently and produces a maximum synthetic jet output when the structural dynamics of the piezoelectric actuator couple with the fluid dynamics and acoustics of the synthetic jet actuator. Early designs of synthetic jet actuators included generally spherical air cavities that were generally similar to the traditional spherical Helmholtz resonators. In these designs, the resonance frequency of the spherical air cavity could be approximated accurately using the Helmholtz resonance equation for vented spheres of air as follows:
                              f          H                =                              v                          2              ⁢                                                          ⁢              π                                ⁢                                    A                                                V                  0                                ⁢                                  L                  eq                                                                                        (        1        )            
Where fH is the Helmholtz resonance frequency, ν is the speed of sound in a gas which is approximately 343 m/s (approximately 1125 ft/s) at 20° C. (68° F.) and at sea level, A is the cross-sectional area of the neck or opening, VO is the static volume of the air cavity, and Leq is the equivalent length of the neck with end correction according to the equation Leq=Ln+0.6d, where Ln is the actual length of the neck and d is the hydraulic diameter of the neck.
Over time, synthetic jet actuators have been developed that have varying air cavity geometries, such as cubic air cavities and cylindrical air cavities. However, current design methods continue to use the Helmholtz resonance equation for estimating the resonance frequency of the non-spherical air cavities. The Helmholtz resonance equation provides a starting point for designing modern synthetic jet actuators, but the equation is a less accurate predictor of the resonance frequencies of non-spherical air cavities than spherical air cavities. In view of this, a need exists for improved design processes for coupling the structural dynamics of the piezoelectric actuators with the fluid dynamics and acoustics of the geometries of the synthetic jet actuators in which they are implemented.